This new book discusses the very latest developmens in modelling, simulation and control of flexible robot manipulators. Coverage includes an overall review of previously developed methodologies, a range of modelling approaches including classical techniques, parametric and neuromodelling approaches, numerical modelling/simulation techniques and more.
Inspec keywords: force control; manipulators; three-term control; finite difference methods; finite element analysis; position control; neural nets
Other keywords: decoupling control; soft computing approach; multi-link flexible manipulator; single-link flexible manipulators; SCEFMAS; open-loop control; force control; position control; space manipulators; collocated control; noncollocated control; finite element simulation; PID control; rigid flexible manipulators; symbolic manipulation; finite difference simulation; smart material flexible manipulators
Subjects: Differential equations (numerical analysis); Spatial variables control; Manipulators; Mechanical variables control; Finite element analysis
This chapter presents a general overview of previously developed methodologies for modelling, simulation and control of flexible manipulators. A selection of currently available flexible manipulator experimental systems in various research laboratories and outside laboratory environments are introduced and their features and design merits described. A structured overview of common applications and future research prospects and applications of flexible and hybrid manipulators are provided.
In this chapter, an analytical model of a single-link flexible manipulator, characterised by a set of infinite number of natural modes, is first developed. This is used to develop state-space and equivalent frequency-domain models of the system. These models can further be used for controller design exercises. An experimental flexible manipulator system is used for identifying model parameters. The model parameter identification procedure involves spectral analysis of collected input-output data from the experimental system. The identified parameters are then used with the developed model and the model response is verified with the experimental system.
This chapter presents a dynamics modelling approach for flexible robotic manipulators. The driving motivation for this chapter is to understand the dynamics of such systems from a control point of view. A general framework is presented that provides an adequate basis for analysis and control of flexible manipulators aimed at terrestrial or orbital applications. To this end, the generalized coordinates chosen to describe the elastic deformation are based on the Ritz approximation, and the approach to arrive at the dynamics model of a single flexible link is the principle of virtual powers, or Jourdain's principle, leading to a Lagrangian description for the elastic deformation and a Eulerian description for the rigid-body motion. A rigid flexible-rigid body is modelled. The evolution to the multi-link case is then natural considering the topology of a serial link manipulator. Two procedures are presented, the first is the O(N3) composite inertia method and the second is the O(N) articulated body method.
This chapter presents the development of parametric and non-parametric approaches for dynamic modelling of a single-link flexible manipulator system. The least mean squares, recursive least squares and genetic algorithms are used to obtain linear parametric models of the system. Non-parametric models of the system are developed using a non-linear autoregressive process with exogeneous input model structure with multi-layered perceptron and radial basis function neural networks. The system is in each case modelled from the input torque to hub-angle, hub-velocity and end-point acceleration outputs. The models are validated using several validation tests. Finally, a comparative assessment of the approaches used is presented and discussed in terms of accuracy, efficiency and estimation of vibration modes of the system.
This chapter presents numerical approaches based on finite difference (FD) and finite element (FE) techniques for dynamic simulation of single-link flexible manipulator systems. A finite-dimensional simulation of the flexible manipulator system is developed using an FD discretisation of the dynamic equation of motion of the manipulator. A methodology is then presented for obtaining the dynamic model of a lightweight flexible manipulator using FE/Lagrangian technique. Structural damping, hub inertia and payload are incorporated in the dynamic model, which is then represented in a state-space form. Simulation results characterising the dynamic behaviour of the manipulator are presented and discussed for both FD and FE methods. A comparative study of the FD and the FE methods of dynamic modelling of flexible manipulators on the basis of computational accuracy, efficiency and demand are then considered. The performance of the algorithms is assessed with experimental results in time and frequency domains.
The application of a symbolic manipulation approach for modelling and analysis of a flexible manipulator system has been presented. It has been demonstrated that the approach provides several advantages in characterising the dynamic behaviour of the manipulator, and in assessing the stability, response and vibration frequency of the system. The system transfer functions have been obtained in symbolic form and thus interrelations between payload and system characteristics have been investigated. Simulation and experimental results have been presented demonstrating the performance of the symbolic approach in modelling and simulation of flexible manipulator systems.
This chapter deals with the development and validation of tools for simulation of flexible space robotic systems using Symofros, a modelling and simulation software program that was developed at the Robotics Section of the Canadian Space Agency. The first part of the chapter describes general modelling issues, Symofros' soft ware architecture, and advanced modelling techniques for flexible arms. The second part presents an experimental validation of the flexible-link model used in Symofros. Additionally, an experimental approach for the end-point detection of flexible links will be discussed. The third part introduces the special purpose dextrous manipulator (SPDM) test verification facility, which is used to emulate the contact dynamic effects arising during pay load insertion and extraction tasks of the SPDM on-board the International Space Station (ISS) based on hardware-in-the-loop simulation. Furthermore, an on-board training simulator that is used by astronauts to evaluate their ability to operate the robotic arm on-board the ISS will be introduced.
This chapter presents the development of open-loop command-generation techniques for control of flexible manipulators based on filtered input, Gaussian shaped input and input shaping and provides a comparative assessment of the performance of these techniques. It is assumed that the motion itself is the main source of system vibration. Thus, input torque profiles that do not contain energy at system natural frequencies will not excite system resonances and hence will not result in structural vibration. Accordingly, shaped torque inputs, including Gaussian shaped, low-pass and band-stop filtered torque input functions and input shaping profiles are developed on the basis of identified resonance modes of the system using parametric and non-parametric modelling methods. Experimental results verifying the performance of the developed control strategies are presented and discussed. Performances of the techniques are assessed in terms of level of vibration reduction at the natural frequencies, time response specifications and robustness to natural frequency variation. The effects of various loading conditions on the performance of the system are also studied.
This chapter provides an overview of the use of real-time command shaping to limit vibration inflexible robotic systems. Smoothing of commands to reduce system vibration is an old idea. However, command shaping did not come into widespread use until inexpensive digital controllers were available to implement the techniques in real time. Shaped commands can address multiple resonant frequencies and can be designed to be very robust to system modelling errors. An array of examples illustrate the effect that these command shaping methods have on the performance of flexible systems.
Industrial control applications have been dominated by the use of proportional, integral, derivative (PID)-type algorithms and are likely to remain so in the near future. This chapter adds a modern flavour to the traditional usage by describing recent PI-PD control strategies, and extending the methodology into a discrete-time multi-input multi-output (MIMO) version. The algorithm can be cast as a general second-order linear regulator and its parameters can thus be systematically chosen by pole-placement. More importantly, the design permits the derivation of an appropriate multivariable decoupling strategy. This is a key improvement and the effectiveness of the proposed multivariable controller has been validated experimentally in real-time motion tracking and vibration control of an asymmetrical flexible manipulator moving in the horizontal and vertical planes under gravity. The PI-PD control performance can be comparable to that of a decoupling MIMO pole-placement controller while being less sensitive to initial transient errors and having a simpler implementation.
While several control schemes have been proposed for force and position control of rigid robot manipulators, only a few related to flexible manipulators have been published so far. In this chapter the main force and position control strategies for flexible manipulators are surveyed and two different approaches are illustrated in depth. One achieves force and position regulation in an indirect way, by computing the joint and deflection variables in the presence of an external contact via a suit able closed-loop inverse kinematics scheme. The other exploits singular perturbation techniques to design force and position control schemes similar to those adopted for rigid robot manipulators, with an additional control action used to stabilise the fast dynamics related to link flexibility. A planar two-link flexible manipulator in contact with a compliant surface is considered, and simulation studies demonstrating the performance of the control techniques are presented and discussed.
This chapter presents the development of closed-loop control strategies for flexible manipulator systems based on collocated and non-collocated control. A closed-loop control strategy using hub-angle and hub-velocity feedback for rigid-body motion control and end-point acceleration feedback forflexural motion control is considered. This is then extended to an adaptive collocated and non-collocated control mechanism using online modelling and controller design. Proportional, integral, derivative (PID) type as well as inverse-model control techniques are considered for flexural motion control. The non-minimum phase behaviour of the plant in the latter case is addressed through conventional techniques. This is further addressed through development of an adaptive neuro-inverse model strategy. The control strategies thus developed are verified and their performances assessed through simulated and experimental exercises.
It is well known that conventional robot manipulators made of rigid links incorporate strongly coupled dynamics, and this situation is the source of many control problems. This difficulty is more pronounced when considering the control of flexible link manipulators. Taking into account the physical properties of flexible manipulators and their inherent vibratory behaviour it is proposed in this chapter to consider the control problem in the multivariable frequency domain. Such an approach is first introduced for analysing the coupling of a mixed rigid-flexible two-dimensional (2D) manipulator. The approach is then extended to the case of a 2D flexible manipulator. Following these analyses, a figure of merit to quantify the interaction between links is introduced, and the resultant designs for obtaining row and column dominance of both 2D manipulators are presented. Finally, an approach involving the manipulator Jacobian is proposed to define the control law. Finite element analysis is used in all cases to simulate the manipulators, and the models are experimentally validated.
This chapter describes modelling and control of space manipulators with flex ble links. The chapter begins with the mathematical model of space manipulators, highlighting differences between control problems of flexible manipulators in space and on the ground. A methodology of stable manipulation-variable feedback control of space manipulators with flexible links for positioning control to a static target and continuous path tracking control is discussed. To avoid instability of direct manipulation-variable feedback, a virtual rigid manipulator (VRM) concept is introduced and a pseudo-resolved-motion-rate control (pseudo-RMRC) for flexible manipulators is derivedfrom the RMRCfor rigid manipulators. Using the VRM, other controls for rigid manipulators are extended to those for flexible manipulators, which can be transformed into joint-variable feedback controls, and are robust stable. For the path tracking control, their orbital stability is discussed in terms of the singular perturbation method. Numerical simulations and hardware experiments of flexible space manipulators successfully demonstrate the effectiveness and feasibility of the proposed method.
The aim of this chapter is to show the effectiveness of soft computing in the design of adaptive controllers for a single-link, flexible manipulator. The first part utilizes fuzzy logic (FL) and genetic algorithms (GAs) in the design of an offline modular neural network controller while the second part combines fuzzy logic and GAs in the construction of online proportional derivative (PD), proportional, integral (PI) and proportional, integral, derivative (PID)-type FL controllers. Experimental results, demonstrating the effectiveness of the methods for an experimental single-link, flexible manipulator are presented and discussed.
In this chapter, dynamic modelling and control of smart material robots are investigated. First, dynamic modelling of a single-link smart material robot is introduced. Then, model-free control is presented for the system without employing the dynamics of the system explicitly. The non-model-based controllers are independent of system parameters and thus possess stability robustness to system parameter uncertainties. Finally, tracking problem of smart material robots is solved by employing singular perturbation techniques. Through the active stabilisation of the fast vibration related variables by smart material actuators, direct control of link deflection is possible and better control performances are expected. Simulation results are provided to show the effectiveness of the presented approaches.
Dynamic modelling and control of manipulators involving both rigid and flexible links are presented in this chapter. Various modelling approaches are discussed, and as an example, the equations of motion of a rigid-flexible two-link manipulator are derived using Hamilton s principle. Discretisation of the governing equations and the effects of coupling between rigid and flexible degrees of freedom are examined. The response to an impact with a rigid surface is studied to investigate the effect of link flexibility on the dynamic response. Various control strategies used in rigid-flexible manipulators are reviewed. As an example, the performance of a non-model-based independent joint proportional, derivative (PD) control is demonstrated. Trajectory tracking and various implementation issues are also discussed.
The focus in this chapter is on a design environment for modelling and control of flexible-link robots. The environment consists of physical equipment and a software environment for design and analysis. The physical equipment comprises two computer platforms, a design platform for analysis and design and, a real-time Linux platform for controlling a laboratory rig equipped with actuator and sensing systems. The rig has several configurations including a horizontal and a vertical mounting of the robot, and is controlled from a real-time Linux platform. The software environment for design, analysis and simulation is based on a Matlab/Simulink workbench extended with a mechatronic Simulink library (MSL). This allows combination of different principles of modelling and control resulting in various control designs and strategies. A simple switch can change the configuration from simulation to real-time application. The real-time code can be generated using real-time workshop (RTW) and transferred to the real-time platform in order to perform the experiments. The collected data can also be transmitted back to the design platform for further analysis.
This chapter presents the development of SCEFMAS (Simulation and Control Environment for Flexible MAnipulator Systems) software package. This is a user-friendly interactive software environment based on Matlab and associated tool boxes. The environment incorporates a finite difference (FD) simulation algorithm of a constrained planar single-link flexible manipulator system for analysis, simulation, modelling of dynamic behaviour of the system. The package also incorporates a range of control techniques, including open-loop control such as filtered command, Gaussian-shaped and command shaping, collocated and non-collocated closed-loop control methods of fixed and adaptive types, and intelligent soft computing control techniques. The environment allows the user to set-up the system by providing its physical parameters and to select the controller type through an interactive graphical user interface (GUI). Data analyses can be performed in time and frequency domains on the controller and system input and outputs signals. The environment is suitable as an education package as well as for research purposes for investigating and developing various simulations, modelling and controller designs for flexible manipulator systems.